How to resolve : increase max function value in fitting using fminsearch?

Hi

I was trying to fit my data with fminsearch function with following code:

f = @(a,b,c,x) a - b.*(x).^c;
obj_fun = @(params) norm(f(params(1), params(2), params(3), x) -y);
sol = fminsearch(obj_fun, [1,1,1]);

err = .02*ones(size(x));
errorbar(x,y,err,'horizontal','s',"MarkerFaceColor",[0.8500, 0.3250, 0.0980], ...
    "MarkerSize",4,"CapSize",4,"Color",[0.8500, 0.3250, 0.0980],"LineWidth",1)
hold on
x = linspace(min,max,20);
plot(x,f(sol(1),sol(2),sol(3),x),'-',"Color",[0.8500, 0.3250, 0.0980],"LineWidth",1)
hold off

Its getting the fit, but I think this is not best optimum fit its showing following message:

 Exiting: Maximum number of function evaluations has been exceeded
         - increase MaxFunEvals option.
         Current function value: 2.586758 

it will be realy great if some experties help me here to take care of this. Im attaching data here (data.txt).

Is there any other function which I can use instade of this to fit and better gobal optimazation.

Thank you in advance!

Answer 1

[Matt J]

You could do as the message says and increas MaxFunEvals, but for your model, it would be better to download fminspleas,

https://www.mathworks.com/matlabcentral/fileexchange/10093-fminspleas

[x,y]=readvars('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1034515/data.txt');

funlist={1,@(c,xd) -xd(:).^c};

[c,ab]=fminspleas(funlist, 1 ,x, y);

sol=[ab(:).',c]

sol = 1×3

-6.5546 -0.0000 -6.0133

[Somnath Kale]

@Matt J thank you for your response!

Can you little bit elaborate the code, means fminsplease function and how your calculation that will be god to understand me as well!

[Matt J]

Fminspleas uses a technique which only needs to iterate over the c parameter, so it is an easier search.

Answer 2

[Matt J]

If you have the Curve Fitting Toolbox,

[x,y]=readvars('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1034515/data.txt');

ft=fit(x(:),y(:),'power2')

ft = 
     General model Power2:
     ft(x) = a*x^b+c
     Coefficients (with 95% confidence bounds):
       a =   1.124e-06  (-2.414e-05, 2.639e-05)
       b =      -6.015  (-14.64, 2.609)
       c =      -6.554  (-9.987, -3.121)

plot(ft,x,y)

[Alex Sha]

adding one term "d*x" for fitting function, the result will be much better:

y = a*x^b+c+d*x

Sum Squared Error (SSE): 1.0988630107163
Root of Mean Square Error (RMSE): 0.3494222232194
Correlation Coef. (R): 0.970379925110827
R-Square: 0.941637199058095

Parameter	Best Estimate    	Std. Deviation     	Confidence Bounds[95%]
---------	-------------    	--------------     	----------------------------------
a        	430058778433358  	0.125126556164325  	[430058778433358, 430058778433359]
b        	14.4836582099507 	3.10784213390318   	[6.49469567251403, 22.4726207473875]
c        	18.5003218509943 	36.6945561128952   	[-75.8260375595516, 112.82668126154]
d        	-257.754044491992	1.5875823760405E-17	[-257.754044491992, -257.754044491992]

[Alex Sha]

or the function: y=a*x^b+c+d*exp(e*x);

Sum Squared Error (SSE): 0.798012086224085
Root of Mean Square Error (RMSE): 0.297771740735171
Correlation Coef. (R): 0.978578556003836
R-Square: 0.957615990270552

Parameter	Best Estimate       	Std. Deviation     	Confidence Interval[95%] (Diff-OK)
---------	-------------       	--------------     	----------------------------------
a        	-3.96448222151296E-7	7.34052972781328E-6	[-2.07770260544974E-5, 1.99841296101948E-5]
b        	-7.72186291539508   	6.95514357122107   	[-27.0324372396597, 11.5887114088695]
c        	-1.28127707754111   	12.6536549323532   	[-36.4134553773351, 33.8509012222529]
d        	286678.994342762    	1537623.25203099   	[-3982447.55739699, 4555805.54608251]
e        	-97.6137053829133   	77.3303025621153   	[-312.317045414963, 117.089634649136]

[Somnath Kale]

@Alex Sha I canot add one more variable which may chage my fiiting model assumptions. can you plese suggest any other function with which I can proceed?

[Matt J]

@Sonnath what is unacceptable about the fit that your current model gives you? You'll notice that both fit() and fminspleas() are in agreement on the fitted parameters.

[Somnath Kale]

@Matt J Im more intrested in fitting coefficint than that the good visual fit. I tried with fminplease it doing the job!

Thanks! looking forword to your help in future as well!